Proposition REF 
shows that the notion of computable discontinuity is also formally related to the notion of productivity.
Weihrauch has introduced a topological and a computability theoretic notion of productivity for subsets \(A\subseteq {{N}}^{{N}}\)  [1]},
[2]}.
If, in a similar way, we transfer the definition of completely productive sets, as originally defined by Dekker [3]},
then we could say that non-open \(A\subseteq {{N}}^{{N}}\)  is completely productive if \(\Delta _A\)  is computable.
Using this terminology, non-open \(A\subseteq {{N}}^{{N}}\)  is completely productive if and only if \(\chi _A\)  is computably discontinuous by Proposition REF .
Myhill [4]} proved that a set \(A\subseteq {{N}}\)  is productive if and only if \(A\)  is completely productive (see also the proofs in [5]}, [2]}).
It is clear that complete productivity for \(A\subseteq {{N}}^{{N}}\)  implies productivity.
We leave it as a task to the reader to study whether productivity also implies complete productivity for Baire space \({{N}}^{{N}}\)  (or even more general spaces).
